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discretized rotation

Ergodic Theory and Dynamical Systems (1)

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Periodic expansion of one by Salem numbers
Part of
SHIGEKI AKIYAMA, HACHEM HICHRI
Journal:

Ergodic Theory and Dynamical Systems / Volume 43 / Issue 9 / September 2023

Published online by Cambridge University Press:

14 October 2022, pp. 2841-2862

Print publication:

September 2023
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We show that for a Salem number $\beta $ of degree d, there exists a positive constant $c(d)$ where $\beta ^m$ is a Parry number for integers m of natural density $\ge c(d)$. Further, we show $c(6)>1/2$ and discuss a relation to the discretized rotation in dimension $4$.